An enhanced one-dimensional mathematical model for simulating flood levels and calculating stage-discharge relationships is presented. Enhanced conveyance subroutines have been developed and incorporated into the commercially available river modelling software ISIS. The newly developed software has been verified using experimental and field data. When a river overtops its banks there is a vigorous interaction between slow moving flood plain flow and faster moving main channel flow. This interaction mechanism has been the focus of intense research over the past forty years. A selective review of this research is detailed with particular attention to the case of meandering channels. The Ackers Method and the James and Wark Method are two discharge capacity methods that have emanated from this recent research and are considered to be the most practically suitable methods and are indeed recommended by the Environment Agency of England and Wales. The methods account for interaction effects when flow is overbank in a straight and meandering channel respectively. It is these methods that have been incorporated into the commercially available and industry leading one-dimensional river model ISIS to enable an enhanced conveyance calculation. The newly developed software has been tested against the Flood Channel Facility Series A and B experiments to a satisfactory level of accuracy. The testing included predicted of stage discharge relationships and water level prediction. In addition it has been applied to the River Dane in Cheshire which is highly meandering and suited to the James and Wark methodology. This was intended to give practical advice concerning the use of the James and Wark Method and the degree of accuracy in estimating the 'channel parameters' which are required by this method. The results of this work showed that a significant rise in water level prediction is obtained when using the enhanced code. Also, it was clear that a high degree of accuracy was not required in estimating the 'channel parameters' with the possible exception of the sinuosity term.